Error computing limits as x -> inf
10-12-2014, 06:26 AM
Post: #12
 parisse Senior Member Posts: 1,322 Joined: Dec 2013
RE: Error computing limits as x -> inf
The algorithm for giac and the Prime is the mrv, aka most rapidly varying variable.
It can handle pretty complicated limit, my regression tests are:
Code:
 limit( exp(x)*(exp(1/x-exp(-x))-exp(1/x)), x=+infinity); limit( exp(x)*(exp(1/x+exp(-x)+exp(-x**2))-exp(1/x-exp(-exp(x)))), x=+infinity); limit( exp(exp(x-exp(-x))/(1-1/x))-exp(exp(x)), x=+infinity); limit( exp(exp(exp(x)/(1-1/x)))-exp(exp(exp(x)/(1-1/x-ln(x)**(-ln(x))))), x=+infinity); limit( exp(exp(exp(x+exp(-x))))/exp(exp(exp(x))), x=+infinity); limit(exp(exp(exp(x)))/exp(exp(exp(x-exp(-x)))),x=+infinity); limit(exp(exp(exp(x)))/exp(exp(exp(x-exp(-exp(exp(x)))))),x=+infinity); limit(exp(exp(x))/exp(exp(x-exp(-exp(exp(x))))),x=+infinity); limit(x*ln(x)*ln(x*exp(x)-x**2)**2/ln(ln(x**2+2*exp(exp(3*x**3*ln(x))))),x=+infinity); limit((exp(x*exp(-x)/(exp(-x)+exp(-2*x**2/(x+1))))-exp(x))/x,x=+infinity); limit((3**x+5**x)**(1/x),x=+infinity); limit(x/ln(x**(ln(x)**(ln(2)/ln(x)))),x=+infinity); limit(exp(exp(2*ln(x**5+x)*ln(ln(x))))/exp(exp(10*ln(x)*ln(ln(x)))),x=+infinity); limit((exp(4*x*exp(-x)/(1/exp(x)+1/exp(2*x**2/(x+1))))-exp(x))/exp(x)**4,x=+infinity); limit(exp(x*exp(-x)/(exp(-x)+exp(-2*x**2/(x+1))))/exp(x),x=+infinity); limit( exp(exp(-x/(1+exp(-x))))*exp(-x/(1+exp(-x/(1+exp(-x)))))*exp(exp(-x+exp(-x/(1+exp(-x)))))/exp(-x/(1+exp(-x)))**2-exp(x)+x, x=+infinity); limit( (ln(ln(x)+ln(ln(x)))-ln(ln(x)))*ln(x)/ln(ln(x)+ln(ln(ln(x)))), x=+infinity); limit(exp(ln(ln(x+exp(ln(x)*ln(ln(x)))))/ln(ln(ln(exp(x)+x+ln(x))))),x=+infinity); limit(exp(x)*(sin(1/x+exp(-x))-sin(1/x+exp(-x**2))),x=+infinity); limit(exp(exp(x))*(exp(sin(1/x+exp(-exp(x))))-exp(sin(1/x))),x=+infinity); limit( (exp(x*exp(-x)/(exp(-x)+exp(-2*x**2/(x+1))))-exp(x))/x,x=+infinity); limit( ln(ln(x*exp(x*exp(x))+1))-exp(exp(ln(ln(x))+1/x)), x=+infinity); limit(sqrt(x+sqrt(x))-sqrt(x),x=+infinity); limit(sqrt(x+sqrt(x+sqrt(x)))-sqrt(x+sqrt(x)),x=+infinity); limit(4/9*exp(exp(5/2*x**(-5/7)+21/8*x**(6/11)+2*x**(-8)+54/17*x**(49/45)))**8/ln(ln(-ln(4/3*x**(-5/14))))**(7/6),x=+infinity); limit(ln(x)**2*exp(sqrt(ln(x))*ln(ln(x))**2*exp(sqrt(ln(ln(x)))*ln(ln(ln(x)))**3​))/sqrt(x),x=+infinity);
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 Messages In This Thread Error computing limits as x -> inf - Chris Pem10 - 10-09-2014, 04:47 AM RE: Error computing limits as x -> inf - Joe Horn - 10-09-2014, 05:59 AM RE: Error computing limits as x -> inf - Chris Pem10 - 10-09-2014, 01:28 PM RE: Error computing limits as x -> inf - Joe Horn - 10-09-2014, 03:52 PM RE: Error computing limits as x -> inf - Chris Pem10 - 10-09-2014, 06:45 PM RE: Error computing limits as x -> inf - Chris Pem10 - 10-10-2014, 05:51 PM RE: Error computing limits as x -> inf - dbbotkin - 10-11-2014, 02:35 AM RE: Error computing limits as x -> inf - Chris Pem10 - 10-11-2014, 01:37 PM RE: Error computing limits as x -> inf - parisse - 10-11-2014, 07:37 AM RE: Error computing limits as x -> inf - dbbotkin - 10-11-2014, 03:02 PM RE: Error computing limits as x -> inf - Chris Pem10 - 10-11-2014, 09:11 PM RE: Error computing limits as x -> inf - parisse - 10-12-2014 06:26 AM

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